Mathematics

# In the figure, $x:y:z=5:4:6$. If $XOY$ is a straight line, find the values of $x,y$ and $z$

##### SOLUTION
From the figure it is given that
$x:y:z=5:4:6$
We can also write it as
$x+y+z=5+4+6=15$
It is given that $XOY$ is a straight line
So we know that
$x+y+z={ 180 }^{ o }$

As we know that the sum of ratio is $15$ then we can write that the measure of $x$ as $5$
The sum of all the angles in a straight line is ${ 180 }^{ o }$
So we get the measure of $x$ as
$x=(5/15)\times 180$
$x=60$

As we know the sum of ratio is $15$ then we can write that the measure of $y$ as $4$
The sum of all the angles in a straight line is ${ 180 }^{ o }$
So we get the measure of $y$ as
$y=(4/15)\times 180$
$y=48$

In order to find $z$ we know that
$x+y+z={ 180 }^{ o }$
Substituting the values of $x$ and $y$ we get
${60}^{o}+{48}^{o}+z={ 180 }^{ o }$
$z={ 180 }^{ o }-{60}^{o}-{48}^{o}$
$z={72}^{o}$

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Subjective Medium Published on 09th 09, 2020
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